The average rent across the country now stands at €987 per month.
New figures by the Residential Tenancies Board show they have risen by just over 7% in the first quarter of this year, meaning the rate of increase has slowed.
However, the cost of renting apartments in Dublin has dropped by 1.5% this quarter.
Director of the Residential Tenancies Board Rosalind Carroll says rents are high across the board.
She said: "Somewhere like Cork city could be something like €1,024 depending on the particular region of the city.
"In Limerick, the rent across three LEA areas averaged between €880 and upwards towards €913."
But the Residential Tenancy Board (RTB) said it’s still too early to say if the slowdown is linked to the introduction by the Government last year of rent pressure zones (RPZs) — a move which capped hikes in high-rent areas.
The first figures since the introduction of RPZs, show while rent rates in Dublin dropped slightly in the first quarter of the year compared to the same period last year, the capital’s rental rates are still running at 8% above their late 2007 peak.
Private renters in other major cities, including parts of Cork and Galway, are also paying up to 8% above the average national rent which now stands at €987 a month — up €1 on the previous quarter.
However, while rents nationally continue to trend upwards, the data shows that quarterly growth was relatively flat, increasing by just 0.1%, down from 2.8% the previous quarter.
RTB director, Rosalind Carroll, said the findings for the first quarter of 2017 suggest the rate of increase in private rents is moderating.
The new figures show no additional parts of the country meet the criteria to be designated RPZs.
Former housing minister (now foreign affairs) Simon Coveney will today launch a public consultation on the review of the rent predictability measure and the RPZs system.
Meanwhile, a report by the Central Bank says house prices — which are expected to rise by a further 10% this year — are “not currently overvalued”.